Phase induced transport of a Brownian particle in a periodic potential in the presence of an external noise: A semiclassical treatment

2011 ◽  
Vol 52 (7) ◽  
pp. 073302 ◽  
Author(s):  
Satyabrata Bhattacharya ◽  
Sudip Chattopadhyay ◽  
Pinaki Chaudhury ◽  
Jyotipratim Ray Chaudhuri
Keyword(s):  
Periodic Potential ◽  
Brownian Particle ◽  
External Noise

Enhanced Diffusion in a Model of Molecular Motors with Potential Switching

2019 ◽  
Vol 18 (02) ◽  
pp. 1940005 ◽  
Author(s):  
Ryota Shinagawa ◽  
Kazuo Sasaki
Keyword(s):  
Diffusion Coefficient ◽  
External Force ◽  
Molecular Motors ◽  
Periodic Potential ◽  
Brownian Particle ◽  
Molecular Motor ◽  
Free Diffusion ◽  
Enhanced Diffusion ◽  
Additional Peak ◽  
Diffusion Enhancement

Diffusion enhancement is a phenomenon in which the diffusion coefficient of a system is increased by an external force and it becomes larger than that of the force-free diffusion in thermal equilibrium. It is known that this phenomenon occurs for a Brownian particle in a periodic potential under a constant external force. Recently, it was found that diffusion enhancement also occurred in a biological molecular motor, whose moving part could move itself by switching the potentials generated by the other parts. It was shown that the diffusion coefficient exhibited peaks as a function of a constant external force. Here, we report the occurrence of an additional peak and investigate the condition governing its appearance.

OPTIMAL DIFFUSIVE TRANSPORT IN A TILTED PERIODIC POTENTIAL

2001 ◽  
Vol 01 (01) ◽  
pp. R25-R39 ◽  
Author(s):  
BENJAMIN LINDNER ◽  
MARCIN KOSTUR ◽  
LUTZ SCHIMANSKY-GEIER
Keyword(s):  
Diffusion Coefficient ◽  
Numerical Solution ◽  
Periodic Potential ◽  
Brownian Particle ◽  
Planck Equation ◽  
Diffusive Transport ◽  
Noise Strength ◽  
Diffusive Motion ◽  
Potential Mapping ◽  
Cumulative Process

We study the diffusive motion of an overdamped Brownian particle in a tilted periodic potential. Mapping the continuous dynamics onto a discrete cumulative process we find exact expressions for the diffusion coefficient and the Péclet number which characterize the transport. At a sufficiently strong but subcritical bias an optimized transport with respect to the noise strength is observed. These results are confirmed by numerical solution of the Fokker-Planck equation.

scholarly journals Numerical Solution for a Non-Fickian Diffusion in a Periodic Potential

2013 ◽  
Vol 13 (2) ◽  
pp. 502-525 ◽  
Author(s):  
Adérito Araújo ◽  
Amal K. Das ◽  
Cidália Neves ◽  
Ercília Sousa
Keyword(s):  
Diffusion Equation ◽  
Periodic Potential ◽  
Space Dimension ◽  
Numerical Solutions ◽  
Brownian Particle ◽  
Particle Density ◽  
Mean Square Displacement ◽  
Hyperbolic Type ◽  
Fickian Diffusion ◽  
Spatial Shape

AbstractNumerical solutions of a non-Fickian diffusion equation belonging to a hyperbolic type are presented in one space dimension. The Brownian particle modelled by this diffusion equation is subjected to a symmetric periodic potential whose spatial shape can be varied by a single parameter. We consider a numerical method which consists of applying Laplace transform in time; we then obtain an elliptic diffusion equation which is discretized using a finite difference method. We analyze some aspects of the convergence of the method. Numerical results for particle density, flux and mean-square-displacement (covering both inertial and diffusive regimes) are presented.

scholarly journals DIFFUSIVE TRANSPORT IN PERIODIC POTENTIALS: UNDERDAMPED DYNAMICS

2008 ◽  
Vol 08 (02) ◽  
pp. L155-L173 ◽  
Author(s):  
G. A. Pavliotis ◽  
A. Vogiannou
Keyword(s):  
Diffusion Coefficient ◽  
Periodic Potential ◽  
Diffusion Tensor ◽  
Brownian Particle ◽  
One Dimension ◽  
Diffusive Transport ◽  
Periodic Potentials ◽  
Arbitrary Dimensions ◽  
Higher Order Corrections ◽  
Rigorous Method

In this paper we present a systematic and rigorous method for calculating the diffusion tensor for a Brownian particle moving in a periodic potential which is valid in arbitrary dimensions and for all values of the dissipation. We use this method to obtain an explicit formula for the diffusion coefficient in one dimension which is valid in the underdamped limit, and we also obtain higher order corrections to the Lifson-Jackson formula for the diffusion coefficient in the overdamped limit. A numerical method for calculating the diffusion coefficient is also developed and is shown to perform extremely well for all values of the dissipation.

scholarly journals Nonlinear noninertial response of a Brownian particle in a tilted periodic potential to a strong ac force

2000 ◽  
Vol 61 (4) ◽  
pp. 4599-4602 ◽  
Author(s):  
W. T. Coffey ◽  
J. L. Déjardin ◽  
Yu. P. Kalmykov
Keyword(s):  
Periodic Potential ◽  
Brownian Particle

scholarly journals ENSLAVING RANDOM FLUCTUATIONS IN NONEQUILIBRIUM SYSTEMS

1996 ◽  
Vol 10 (28) ◽  
pp. 3857-3873 ◽  
Author(s):  
MANGAL C. MAHATO ◽  
T.P. PAREEK ◽  
A.M. JAYANNAVAR
Keyword(s):  
Periodic Potential ◽  
Brownian Particle ◽  
Physical Models ◽  
Temperature Inhomogeneity ◽  
Stable States ◽  
Inhomogeneous Systems ◽  
Potential System ◽  
Macroscopic Motion ◽  
Random Fluctuations ◽  
Unidirectional Motion

Several physical models have recently been proposed to obtain unidirectional motion of an overdamped Brownian particle in a periodic system. The asymmetric ratchetlike form of the periodic potential and the presence of correlated nonequilibrium fluctuating forces are considered essential to obtain such a macroscopic motion in homogeneous systems. In the present work, instead, inhomogeneous systems are considered, wherein the friction coefficient and/or temperature could vary in space. We show that unidirectional motion can be obtained even in a symmetric nonratchetlike periodic potential system in the presence of white noise fluctuations. We consider four different cases of system inhomogeneity. We argue that all these different models work under the same basic principle of alteration of relative stability of otherwise locally stable states in the presence of temperature inhomogeneity.

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